My younger daughter Yani was 3 time California state finalist (8th place best result).

The school competition usually starts right after winter break.

I don't know if you have following books or not. These are the standard equipments for all serious Geobee contestants.

http://shop.nationalgeographic.com/product/767/4223/767.html
http://shop.nationalgeographic.com/product/767/2335/767.html

Assuming that your son win the school competition which may not be easy by itself, he will be invited to a written test. If he does will on this test (individual state decides the cut-off line), he will be invited to state finals.

In state finals, there are 2-3 rounds to decide the winner. Only the winner moves on to national. Others get the bragging rights. It is my observation that those who do well in Geobee are usually very gifted (and hard working too).

Good luck.